Geodesic
On spectral domain of periodically correlated processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 2, pp. 398-405 Cet article a éte moissonné depuis la source Math-Net.Ru

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The content of this article primarily falls into three sections. Section 1 deals with a basic structural spectral representation theorem for periodically correlated sequences. Section 2 provides a certain class of square integrable functions that is isomorphic to the time domain of the sequence. This complete class is called the spectral domain of the sequence. Section 3 is related to the unsuccessful previous attempts by others to construct a complete function space as the spectral domain. These are natural extensions of the known results for the stationary case to the periodically correlated sequences.
Keywords: periodically correlated sequence, completeness.
Mots-clés : spectral domain 
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A. Makagon; A. Miamee; H. Salehi; A. Soltani. On spectral domain of periodically correlated processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 2, pp. 398-405. http://geodesic.mathdoc.fr/item/TVP_2007_52_2_a13/

[1] Adams G. T., McGuire P. J. Paulsen V. I., “Analytic reproducing kernels and multiplication operators”, Illinois J. Math., 36:3 (1992), 404–419 | MR | Zbl

[2] Chang D. K., Rao M. M., “Bimeasures and nonstationary processes”, Real and Stochastic Analysis, ed. M. M. Rao, Wiley, New York, 1986, 7–11 | MR

[3] Cramér H., “A contribution to the theory of stochastic processes”, Proceeding of the Second Berkeley Symposium on Mathematical Statistics and Probability, Univ. of California Press, Berkeley–Los Angeles, 1951, 329–339 | MR

[4] Danford N., Shvarts Dzh., Lineinye operatory: Obschaya teoriya, IL, M., 1962, 895 pp.

[5] Gladyshev E. G., “O periodicheski korrelirovannykh sluchainykh posledovatelnostyakh”, Dokl. AN SSSR, 137:5 (1961), 1026–1029 | Zbl

[6] Makagon A., Miamee A. G., Salehi H., “Periodically correlated processes and their spectrum”, Nonstationary Stochastic Processes and Their Applications, World Scientific, River Edge, 1992, 147–164 | MR

[7] Makagon A., Salehi H., Is the spectral domain of a periodically correlated sequence complete?, Technical Report RM-529, Department of Statistics and Probability, Michigan State University, 1993

[8] Miamee A. G., “Periodically correlated processes and their stationary dilations”, SIAM J. Appl. Math., 50:4 (1990), 1194–1199 | DOI | MR | Zbl

[9] Miamee A. G., Salehi H., “An example of a harmonizable process whose spectral domain is not complete”, Scand. J. Statist., 18:3 (1991), 249–254 | MR | Zbl

[10] Miamee A. G., Soltani A. R., On spectral analysis of periodically correlated stochastic processes, Technical Report, Department of Mathematics, Hampton University, 1995

[11] Rao M. M., “The spectral domain of multivariate harmonizable processes”, Proc. Natl. Acad. Sci. USA, 81 (1984), 4611–4612 | DOI | MR | Zbl

[12] Rozanov Yu. A., Statsionarnye sluchainye protsessy, Fizmatgiz, M., 1963, 284 pp. | MR

[13] Soltani A. R., “A characterization theorem for stable random measures”, Stochastic Anal. Appl., 18:3 (2000), 299–308 | DOI | MR | Zbl

[14] Soltani A. R., Shishebor Z., “A spectral representation for weakly periodic sequences of bounded linear transformations”, Acta Math. Hungar., 80:3 (1998), 265–270 | DOI | MR | Zbl

[15] Wiener N., Masani P., “The prediction theory of multivariate stochastic processes. II: The linear predictor”, Acta Math., 99 (1958), 93–137 | DOI | MR